Faraday's laws of electrolysis

Michael Faraday

Faraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833.

First law

Michael Faraday reported that the mass (Template:Mvar) of a substance deposited or liberated at an electrode is directly proportional to the charge (Template:Mvar, for which the SI unit is the ampere-second or coulomb). $$m\propto Q⟹\frac{m}{Q}=Z$$

Here, the constant of proportionality, Template:Mvar, is called the electro-chemical equivalent (ECE) of the substance. Thus, the ECE can be defined as the mass of the substance deposited or liberated per unit charge.

Second law

Faraday discovered that when the same amount of electric current is passed through different electrolytes connected in series, the masses of the substances deposited or liberated at the electrodes are directly proportional to their respective chemical equivalent/equivalent weight (Template:Mvar). This turns out to be the molar mass (Template:Mvar) divided by the valence (Template:Mvar)

$\begin{array}{cc}& m\propto E;E=\frac{\text{molar mass}}{\text{valence}}=\frac{M}{v}\\ & ⟹m_1:m_2:m_3:\dots =E_1:E_2:E_3:\dots \\ & ⟹Z_{1}Q:Z_{2}Q:Z_{3}Q:\dots =E_1:E_2:E_3:\dots \\ & ⟹Z_1:Z_2:Z_3:\dots =E_1:E_2:E_3:\dots \end{array}$

Derivation

A monovalent ion requires one electron for discharge, a divalent ion requires two electrons for discharge and so on. Thus, if Template:Mvar electrons flow, $\frac{x}{v}$ atoms are discharged.

Thus, the mass Template:Mvar discharged is $$m=\frac{xM}{v{N}_{\mathrm{A}}}=\frac{QM}{e{N}_{\mathrm{A}}v}=\frac{QM}{vF}$$ where

• Template:Math is the Avogadro constant;
• Template:Math is the total charge, equal to the number of electrons (Template:Mvar) times the elementary charge Template:Mvar;
• Template:Math is the Faraday constant.

Mathematical form

Faraday's laws can be summarized by

$Z=\frac{m}{Q}=\frac{1}{F}\left(\frac{M}{v}\right)=\frac{E}{F}$

where Template:Mvar is the molar mass of the substance (usually given in SI units of grams per mole) and Template:Mvar is the valency of the ions .

For Faraday's first law, Template:Mvar are constants; thus, the larger the value of Template:Mvar, the larger Template:Mvar will be.

For Faraday's second law, Template:Mvar are constants; thus, the larger the value of $\frac{M}{v}$ (equivalent weight), the larger Template:Mvar will be.

In the simple case of constant-current electrolysis, Template:Math, leading to

$m=\frac{ItM}{Fv}$

and then to

$n=\frac{It}{Fv}$

where:

• Template:Mvar is the amount of substance ("number of moles") liberated: $n=\frac{m}{M}$
• Template:Mvar is the total time the constant current was applied.

For the case of an alloy whose constituents have different valencies, we have $$m=\frac{It}{F\times \sum _i\frac{w_i{v}_i}{M_i}}$$ where Template:Mvar represents the mass fraction of the Template:Mvarth element.

In the more complicated case of a variable electric current, the total charge Template:Mvar is the electric current Template:Math integrated over time Template:Mvar:

$Q=\underset{0}{\overset{t}{\int }}I(\tau )d\tau$

Here Template:Mvar is the total electrolysis time.

Applications

• Electroplating – a process where a thin layer of metal is deposited onto the surface of an object using an electric current
• Electrochemical cells – generates electrical energy from chemical reactions
• Electrotyping – a process used to create metal copies of designs by depositing metal onto a mold using electroplating
• Electrowinning – a process that extract metals from their solutions using an electric current
• Electroforming – a process that deposits metal onto a mold or substrate to create metal parts
• Anodization – a process that converts the surface of a metal into a durable corrosion-resistant oxide layer
• Conductive polymers – organic polymers that conduct electricity
• Water electrolysis – a process that uses an electric current to split water molecules into hydrogen and oxygen gases
• Electrolytic capacitors – a type of capacitor that uses an electrolytic solution as one of its plates

See also

• Electrolysis
• Faraday's law of induction
• Tafel equation

Further reading

• Serway, Moses, and Moyer, Modern Physics, third edition (2005), principles of physics.
• Experiment with Faraday's laws